The radioactive nuclei ⁶⁰Co is widely used in medical applications.It undergoes beta decay,and the total energy of the decay process is 2.82 MeV per decay event.The half-life of this nucleus is 272 days.Suppose that a patient is given a dose of 6.9 µCi of ⁶⁰Co.If all of this material decayed while in the patient's body,what would be the total energy deposited there? (1 Ci = 3.70 × 10¹⁰ decays/s)

Question

Quizplus · Accepted Answer

First, convert the dose from microcuries (µCi) to decays per second (dps) using the given conversion factor: $6.9 \mu Ci = 6.9 \times 10^{-6} Ci \times 3.70 \times 10^{10} dps/Ci = 2.553 \times 10^{5} dps$. Then, calculate the total energy deposited by multiplying the decay rate by the energy per decay and the time. Since the half-life is 272 days, and we're considering the scenario where all of the material decays, we need to find the total energy without explicitly calculating the time it takes for all to decay. The energy per decay is 2.82 MeV, or $2.82 \times 10^{6} eV/decay \times 1.602 \times 10^{-19} J/eV = 4.51864 \times 10^{-13} J/decay$. The total energy is then $2.553 \times 10^{5} dps \times 4.51864 \times 10^{-13} J/decay \times 272 \times 24 \times 3600 s = 3.9 J$, assuming continuous decay over the 272 days.

The Radioactive Nuclei 60Co Is Widely Used in Medical Applications

The Radioactive Nuclei ⁶⁰Co Is Widely Used in Medical Applications